1. Field of the Invention
The present invention relates to a device and method for generating information representing an arrangement of a set of particles in a particle system simulation.
2. Description of the Related Art
One existing method for analyzing and predicting the nature of a material composed of an inorganic or an organic substance uses a simulation based on a Molecular Dynamics (MD) calculation. To perform this calculation, an initial arrangement of atoms or molecules, which forms the material, must be generated. In the MD calculation, attempts are made to solve a differential equation (e.g., a Newtonian equation) by using a given initial arrangement as an initial value to examine the nature of the system representing the material with a calculation result, and further, to implement the prediction of the nature.
However, experimental data on the arrangement of a system of molecules (the positional coordinates of all of the atoms forming molecules) is not obtained in many cases although the experimental data on a molecule structure considered to be a stable state of one molecule or a density of mass of the molecules at normal temperature and pressure is obtained. Accordingly, it is not known how to generate the initial arrangement of the molecules, which realizes an experimentally obtained density of mass of the molecules, when the MD calculation of a molecule system is performed.
A simple method for generating the initial arrangement of a set of particles in a unit cell is a method, which calculates the number of particles per cell from the experimental data on the density of mass of the particles, and arranges particles in the cell at random. However, if the particles are arranged completely at random, a pair of particles which have a close distance is sometimes generated. It is known that very intense force is applied between the close particles. If even one such pair of close particles exists, the velocity of the particles increase due to an interaction between them, so that the temperature of the system becomes very high locally in the neighborhood of the pair. Accordingly, a very large numerical value occurs when a differential equation is solved, which sometimes leads to a failure of a numerical value integral algorithm.
Three conventional methods to prevent such a simulation failure can be devised. Normally, these methods are combined and used in many cases.
(1) Heat Emission Method
This is a method for emitting heat of a system generated during a simulation at suitable timing. Specifically, the velocity of each particle is decreased or reduced to “0”.
(2) Potential Relaxation Method
This is a method for preventing very intense force from being applied between close particles by weakening an interaction with the transformation of a potential function in a region where a distance between particles is short. With this method, the form of the potential function is continually changed during simulation, and is restored to its original function form by degrees. At this time, if all of the distances between respective particles are (equal to or) larger than a predetermined value Ri as a result of the measurement of the distances between particles, the potential function is restored to the original function form. The value of Ri is input as a parameter beforehand.
(3) Cell Size Change Method
This is a method for starting simulation after setting a cell whose size is larger than a size calculated from the experimental data on a density of mass of the particles. With such a cell, the probability that a pair of particles having a close distance being generated becomes small even if particles are arranged at random. At this time, if a pair of particles, whose distance is smaller than a predetermined value Rd, is found as a result of the measurement of the distances between particles, the particles are rearranged at random. Such a trial is iterated, and a normal simulation is started when all of the distances between particles become (equal to or) larger than Rd.
However, the above described conventional simulation methods have the following problems.
(1) Heat Emission Method
If a given initial arrangement happens to be an arrangement which does not cause a failure of a numerical integral algorithm, a simulation can properly work. However, there is no such guarantee. Thus, this method must be combined with any of the other methods.
Additionally, if heat emission timing is unsuitable, the simulation cannot work properly. If the timing is delayed, the numerical integral algorithm encounters a failure, or numerical errors are accumulated, which can possibly cause a failure. On the contrary, if heat is emitted too often, the velocity of respective particles slow down, so that time development of the system change becomes slow, which leads to a high calculation cost.
(2) Potential Relaxation Method
It is not easy to set parameters (such as a parameter for specifying transformation timing, and a parameter for specifying a transformed function form), and know-how is required. Although an empirically determined setting may be sometimes available, the simulation cannot properly work depending on a target system. Therefore, trial and error for setting parameters is required in many cases. Additionally, these parameters must be set for each pair of atom types so as to be effectively set. However, this setting operation becomes complex if a system is complicated.
Furthermore, it is also important that a determination condition for restoring a potential function should be suitably set. When a “go” determination for restoring a potential function to its original form is made before entering a fully equilibrium state, an extra calculation cost can possibly be incurred.
To explain this, FIG. 1A shows a simulation result which is obtained as a result of combining the heat emission and the potential relaxation methods, applied to a system of alkane molecules. In FIG. 1A, the horizontal axis represents a time (different from a calculation time) describing a physical change in a system, “U” represents the value (gA2 fs−2) of a potential function (internal energy), “V” represents the volume (A3) of a cell, and “T” represents a temperature (K).
In this example, a “go” determination is made in the neighborhood of 0.6×10−1 ps. However, since its timing is unsuitable, intense force is applied between particles after the “go” determination is made. As a result, the volume “V” of the cell is expanded. Therefore, a considerable calculation cost is required until the volume “V” approaches the value based on experimental data.
Additionally, if an interaction is not a 2-body force, the operation for transforming a potential function is difficult to be formulated.
(3) Cell Size Change Method
If a cell size is not sufficiently large, the number of times that the trial of a random arrangement for generating an initial arrangement is iterated increases, which leads to complications. However, if the cell size is too large, a lot of time is taken to restore the cell to its original size by means of experimental data. In a system where an interaction is complicated and the number of particles is large as in a system of macromolecules, the cost of the restoration is high. It may sometimes be necessary to make a calculation for several hours in a supercomputer until a density of mass of the molecules calculated from a cell size approaches experimental data.
Suppose that the simulation result shown in FIG. 1B is obtained as a result of applying the cell size change method to a system of 20 liquid crystal molecules. In FIG. 1B, the time represented by the horizontal axis and “U”, “V”, and “T” are the same as those shown in FIG. 1A. In this example, a calculation is required to be processed for many hours until the volume “V” converges.
As described above, it cannot be said that the method (1) through (3) are truly satisfactory methods from an ease-of-use, a general-purpose, or a calculation cost viewpoint. Therefore, an easy-to-use and highly general-purpose simulation method which never causes an algorithm failure due to a huge numerical value and which requires a low calculation cost is desired.